...Find the area of the section of the ellipsoid *+?+*-i «»^> V made by the plane /.«+?»y+nZ = 0. The sum of the squares of the reciprocals of the areas...of an ellipsoid made by any three diametral planes mutually at right angles to one another is constant. 6. Show that the hyperboloid can be generated...

...perpendicular to CP, where k is a line of constant length ; shew that the equation to the locus of P is 100. The sum of the squares of the reciprocals of the areas...diametral planes at right angles to each other is constant. 101. An ellipsoid and hyperboloid are concentric and confocal ; if a tangent plane be drawn...

...where k is a line of constant length ; shew that the equation to the locus of P is aV + &y+dV-^|p. 100. The sum of the squares of the reciprocals of the areas...diametral planes at right angles to each other is constant. 101. An ellipsoid and hyperboloid are concentric and their principal sections are confocal...

...Article 108, Problem IL From equation 3 it is obvious, that the sum of the normal stresses on a pair of planes at right angles to each other is equal to the sum of tfie principal stresses ; and from equation 4 follows the principle, already demonstrated otherwise...

...the article on shearing stress, Art. XXXIV, such as that the sum of the normal stresses on a pair of planes at right angles to each other is equal to the sum of the principal stresses, and that the shearing stresses on a pair of planes at right angles are equal to...